Former New York Chief Judge Judith Kaye has become the “go to” lawyer these days for dubious outfits that find themselves in hot water.

The shady Working Families Party hired Kaye and her firm, Skadden Arps, to conduct an internal review of its for-profit arm in hopes of forestalling prosecutors’ criminal probes.

And when top brass at the State University system found itself under the gun thanks to the scandal-scarred SUNY-Binghamton basketball program, it, too, turned to Kaye.

SUNY has been taking criticism as the result of Binghamton President Lois DeFleur’s ambitious program to bring big-time basketball to her campus.

DeFleur and Athletic Director Joel Thirer decided their school should move from Division III to the top-level Division I and push hard for a berth in the NCAA tournament.

So they built a $33 million arena and hired a new head coach, Kevin Broadus, to recruit top athletes.

Within two years, Binghamton had made the tournament. But then the school’s hoop dreams turned into a nightmare.

Broadus’ players had been steered into courses like Bowling I and Theories of Softball; when they couldn’t pass even those, their grades were changed. Before long, three of his players had been expelled and two others kicked off the team for arrests ranging from shoplifting to selling crack.

Broadus was fired, Thirer resigned and DeFleur has announced her retirement.

But it wasn’t SUNY — or even Binghamton — that gave Kaye what turned out to be a million-dollar contract. It was the Research Foundation of the State University of New York — whose money is supposed to support instruction and organized research.

Officials say they had the foundation pay so that taxpayer money wouldn’t be used to fund her report. But it also allowed SUNY to get around a state law requiring that such contracts be let out to bid and approved by both the attorney general and the comptroller.

It also meant, according to published reports, that SUNY Chancellor Nancy Zimpher was able to steer the contract directly to Kaye, her preferred choice to head the probe.